西南财经大学工商管理学院;
U型效应在社科领域具有重要研究意义。对U型效应的探索和研究，不但有助于理解变量间复杂关系，揭示变量间内在影响机制，而且还能明晰U型曲线转折点，为实践应用中要素投入的最优值或最优区间提供指导和启示。基于三角函数和双曲函数的独特性质，提出了两种新的表征和检验变量间U型关系的实证模型，即双弦模型和双曲模型。从数学角度对两个新模型进行理论推导和诠释，从实证角度以“企业价值与股权制衡”为题，基于2014—2023年中国A股上市公司样本数据对新模型进行检验，从统计分析角度采用随机抽样回归和随机森林算法对新模型以及传统的平方项模型进行全面性能测评和对比分析。结果表明，两个新模型均能准确刻画变量间U型关系，曲线极值点计算较为便捷。基于10 500次随机抽样回归的测试结果表明，两个新模型的信息损失程度、拟合优度、解释力度等各项指标均较为稳定；与平方项模型相比，两个新模型性能更优，拟合能力和解释力更强，统计分析的显著性标准更严格，采用新模型开展U型效应研究其结果更具可信度。基于随机森林算法的测评结果基本相同。综合权衡各项指标后，双曲模型性能最优，双弦模型次之，平方项模型再次之。
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(1)限于篇幅,剔除样本后的回归结果从略,备索。
基本信息:
DOI：10.20207/j.cnki.1007-3116.20250303.001
中图分类号:F832.51;F272.5;F224
引用信息:
[1]厉双,何杰.两种基于特殊函数的U型效应实证模型[J].统计与信息论坛,2025,40(05):3-19.DOI:10.20207/j.cnki.1007-3116.20250303.001.
基金信息:
国家自然科学基金面上项目“中国上市公司终极实际控制权现实状况、作用机制及其行为后果研究”(71572149)